Why can't pure KG embedding methods discover multi-hop relations paths?
To put this insert to context, we should take at least this much of text from the paper:


  One line of research focuses on making recommendations using knowledge graph embedding models, such as TransE [2] and node2vec [5]. These approaches align the knowledge graph in a regularized vector space and uncover the similarity between entities by calculating their representation distance [30]. However,pure KG embedding methods lack the ability to discover multi-hop relational paths.


In my understanding the pure KG embedding here refers to TransE and node2vec solutions. To learn more about those, we should read links [1] and [2]. From [1]:


  Usually, we use a triple (head, relation, tail) to represent a knowledge. Here, head and tail are entities. For example, (sky tree, location, Tokyo). We can use the one-hot vector to represent this knowledge.


Later on same source there is an explanation on the end of definition section of TransE solution:


  But this model only can take care with one-to-one relation, not suitable for one-to-many/many-to-one relation, for example, there is two knowledge, (skytree, location, tokyo) and (gundam, location, tokyo). After training, the 'sky tree' entity vector will be very close with 'gundam' entity vector. But they do not have such similarity in real.


On other hand, [3] tells:


  Knowledge graphs as described above represents a static snapshot of our knowledge. It does not reflect the process of it’s how the knowledge built up. In the real world, we learn by observing temporal patterns. While it’s possible to learn the similarity between nodes A and node B, it will be hard to see the similarity between node A and node C as it was 3 years ago.


Solution in paper states "--,each recommended item is associated with around 1.6 reasoning paths." which is supposedly impossible for TransE solution.

So, knowledge graph, purely, is a static snapshot that can identify by great accuracy one to one findings. Actually according what [2] tells how node2vec works, they can describe and combine also more information (node2vec combines different types of similarities at same time), but anyways I think the main point is actually in one word in the citation: discover! 

The model suggested on paper adds Reinforcement Learning principles to the KG modeling, so to say, the pure KG embedding always tells one distance based statistical solution, but a RL based solution may learn more aspects behind the scenes as it learns by try and error more complex paths underlying in the behavior.

On the other hand, the paper says, when relating their solution to pure TransE:


  It can be regarded as a single-hop latent matching method, but the post-hoc explanations do not necessarily reflect the true reason of generating a recommendation. In contrast, our methods generate recommendations through an explicit path reasoning process over knowledge graphs, so that the explanations directly reflect how the decisions are generated, which makes the system transparent.


So, whether TransE and those could actually recommend things in the given environment, the recommendation reasoning paths may stay obscure.

Sources:

[1] https://towardsdatascience.com/summary-of-translate-model-for-knowledge-graph-embedding-29042be64273

[2] https://towardsdatascience.com/node2vec-embeddings-for-graph-data-32a866340fef

[3] https://towardsdatascience.com/extracting-knowledge-from-knowledge-graphs-e5521e4861a0